LETTERS
PUBLISHED ONLINE: 18 NOVEMBER 2012 | DOI: 10.1038/NCLIMATE1585
Adaptation of US maize to temperature variations
Ethan E. Butler* and Peter Huybers
High temperatures are associated with reduced crop yields1,2 ,
and predictions for future warming3 have raised concerns
regarding future productivity and food security4–8 . However,
the extent to which adaptation can mitigate such heat-related
losses remains unclear9–13 . Here we empirically demonstrate
how maize is locally adapted to hot temperatures across US
counties. Using this spatial adaptation as a surrogate for future
adaptation, we find that losses to average US maize yields from
a 2 ◦ C warming would be reduced from 14% to only 6% and
that loss in net production is wholly averted. This result does
not account for possible changes in temperature variability or
water resources, nor does it account for all possible forms
of adaptation14–18 , but it does show that adaptation is of
first-order importance for predicting future changes in yield.
Further research should be undertaken regarding the ability to
adapt to a changing climate, including analysis of other crops
and regions, the application of more sophisticated models
of crop development, and field trials employing artificially
increased temperature.
Global maize yields are forecast to decline in response to
increasing temperature, particularly as the upper range of growing
season temperatures become hotter1,2,4–7,19 . The sensitivity of crop
yields to increased temperature is often estimated through analysis
of variability in annual yield and growing season temperature1,2,7,19 ,
but there is a potentially important distinction between year-to-year
anomalies and changes in climate in that the latter can be more
fully adapted to. For instance, US corn hybrids have a product
half-life of about 4 years11 , suggesting sufficiently rapid turnover
to adapt to decadal changes in climate. To explore the adaptability
of maize production to long-term differences in climate, we analyse
the sensitivity of extant crops growing in a range of different climate
conditions and use this spatial variation to develop a functional
form for future adaptation.
We explore yields within the US because relatively high-quality
data and a highly adapted and managed agricultural demographic
can be assumed. Yield data are available from more than 1,600
counties between 1981 and 2008 from the United States Department
of Agriculture/National Agriculture Statistics Service20 in the
Eastern US, and daily temperature is estimated for each county
using a network of 534 weather stations21 for which daily minimum
and maximum surface air temperature is available.
The influence of temperature on yield is parameterized using
growing degree days (GDDs) and killing degree days (KDDs).
GDDs are a commonly used measure for the cumulative warmth a
crop has experienced over the growing season1,15,22,23 , here defined
as the sum of all daily average temperatures over the growing
season in excess of 8 ◦ C. The threshold is in accord with previous
studies1,15 , but we use a new approach to define the growing season
using average planting and harvest dates reported for each state on
each year20 , with the average weighted according to the amount
of planted or harvested crop. Daily temperature is computed by
taking the average of the maximum and minimum temperature at
the nearest available weather station. KDDs are defined similarly
to GDDs, but summing maximum temperatures in excess of 29 ◦ C,
consistent with previous studies1,2,19 . Whereas GDDs are indicative
of higher yields (for example, by enabling a longer period of grain
development), KDDs decrease yield (for example, by accelerating
the plant through grain development or directly damaging plant
tissue or enzymes24,25 ). Note that although 29 ◦ C is a low threshold
for the initiation of damage26 , stressed maize plants have been
shown to experience higher temperatures than the air measured
above the crop canopy27 .
Time series of GDD and KDD anomalies for each county are
linearly combined along with a constant and time-trend term to
represent yield for each county,
Y = β0 + β1 t + β2 GDD0 + β3 KDD0 + (1)
A prime indicates that the sample mean is removed. The β
coefficients are fitted to maximize the variance explained in Y ,
subject to the condition that GDD contributions cannot be negative
(β2 ≥ 0) and KDD contributions cannot be positive (β3 ≤ 0).
The linear time term, t , accounts for technological and other
steady changes over this time period and is the residual error.
Uncertainty estimates are obtained for each of the parameters using
a bootstrapping method.
Fitting the four adjustable parameters in equation (1) to each
county results in an average squared cross-correlation between
predictions and observations of R2 = 0.65 (Supplementary Fig. S1).
For comparison, other recent empirical fits to maize data obtained
an R2 of 0.47 with four adjustable parameters6 and 0.77 using about
20 adjustable parameters1 . An F -test is then used to determine
whether the full model of equation (1) performs significantly better
(P ≤ 0.05) than one containing only the mean and time trend.
Counties with insignificant model fits are omitted, reducing our
pool of counties from more than 1,600 to a subset of 1,013 counties
showing a statistically significant relationship with temperature
variations (Supplementary Fig. S2), although a similar result is
obtained when using the full sample. See the Methods for a further
description of the model and the Supplementary Information for a
more detailed case study.
The sensitivity of yield to GDD has values of 0.15 (bushels
per acre)/GDD in cool northwestern regions of the study domain
and trends to values near zero in the hotter southeastern regions
(Fig. 1a). Yield sensitivity to KDDs (Fig. 1b) is nearly orthogonal
to that of GDDs, trending from more negative than −0.5 (bushels
per acre)/KDD in northeastern regions towards less negative than
−0.2 (bushels per acre)/KDD in southwestern regions. Variations
in the sensitivity to GDDs and KDDs is perhaps unsurprising, given
that maize originated in the tropics and has been adapted to grow
in colder climates25 .
Our focus will be on KDD regional variation in sensitivity and
the consequences of a warming climate. Field trials on cultivars
planted in different regions of the US have demonstrated a pattern
Department of Earth and Planetary Science, Harvard University, Cambridge, Massachusetts 02138, USA. *e-mail: [email protected].
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NATURE CLIMATE CHANGE DOI: 10.1038/NCLIMATE1585
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a
0.0
50° N
¬0.1
(Bushels/acre)/KDD
¬0.2
Latitude
40°
N
30°
¬0.3
¬0.4
¬0.5
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¬0.8
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100° W
0.00
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80° W
90° W
Longitude
0.04
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0.08
0.10
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Yield/growing degree day
0.14
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50° N
b
100
20 0
Latitude
30
0
100
40°
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20
0
500
300
500
0
40
0
40
90° W
Longitude
¬0.3
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Yield/killing degree day
80° W
¬0.1
0.0
Figure 1 | Sensitivity of maize yield to temperature variations. a, Yield
sensitivity to GDDs. b, Yield sensitivity to KDDs (shading) and the
climatological average of KDDs (contours). Counties with at least 10% of
their crop area irrigated are indicated by black borders.
of heat tolerance9 consistent with our findings of lower sensitivity in
hotter climates (Fig. 1b). Cultivars adapted to hot climates produce
more heat-resistant proteins and control for moisture deficits
through greater stomatal sensitivity, osmotic adjustment and
membrane structures that confer drought resistance9–11 . Although
there are other management options that could reduce sensitivity to
temperature, such as developing fields to increase water retention,
the most likely candidate to explain the observed variation in KDD
sensitivity is cultivar selection, and we seek to capture this effect in
the form of a simple function. Note that although another study1
reported lack of evidence for regional variations in yield sensitivity
to high temperatures, further analysis using that study’s approach
gives results consistent with the above reported findings (see the
Supplementary Information).
2
300
400
500
Mean killing degree days
600
700
800
Figure 2 | The climatological average KDDs versus the sensitivity of yield
to KDDs for individual US counties. A logarithmic fit provides a functional
relationship between climatology and sensitivity (red line, equation (2)).
For reference, linear and inverse fits are also included (grey lines) and
would imply greater and lesser ability to adapt to warming, respectively.
Red dashes represent bootstrap 95% confidence intervals. For visual clarity,
data points with 95% confidence interval lengths greater than 0.5 (bushels
per acre)/KDD are not shown as they have little influence on the
weighted fit.
β3 = αo + αln(KDD) + η
6
70 00
0
100° W
¬0.4
200
0
¬0.5
0
40
110° W
20
300
600
N
80
0
200
400
30°
100
We interpret the varied spatial sensitivity to KDDs diagnosed
across US counties as indicative of adaptability. Indeed, there
exists a strong relationship between the climatology of KDDs and
the sensitivity of yield to KDDs for both unirrigated (Fig. 2) and
irrigated crops (Supplementary Fig. S3) that can be approximated
using a logarithmic relationship,
100
300
0
(2)
Equation (2) is fitted to the data by minimizing the sum of η2 ,
where the sum is inversely weighted according to the bootstrapped
variance estimates associated with each sensitivity, β3 . This gives
a base sensitivity of αo = −0.64 (bushels per acre)/KDD (with a
bootstrapped 95% confidence interval (c.i.) of −0.69 to −0.59) and
an adaptation factor of α = 0.08 (bushels per acre)/(KDD ln(KDD))
for unirrigated crops (95% c.i., 0.07–0.09). For irrigated crops
the base sensitivity is much lower, αo = −0.38 (95% c.i.,−0.47 to
−0.28), and adaptation is weaker, α = 0.04 (95% c.i., 0.02–0.06).
Essentially, equation (2) states that hotter counties are less
sensitive to yield losses from heat but that differences in sensitivity
asymptote to zero towards hotter climatologies. This formulation
has the advantage of indicating the greatest change in the most datarich regions and minimal change in the hottest regions, thereby
limiting inferences based on extrapolation. Furthermore, when we
consider a 2 ◦ C warming scenario (Supplementary Fig. S5), only 18
of the 837 unirrigated counties included in this study exceed the
sampled range of the historical climatology, and even though those
counties experience amongst the largest changes in KDD, their
inferred adaptive change in sensitivity averages only 0.03 (bushels
per acre)/KDD, whereas the domain average is 0.05 (bushels per
acre)/KDD. Exclusion of these 18 counties would have no influence
on yield statistics at the reported precision level.
Equation (2) represents a moderate case relative to the greater
and lesser adaptability respectively implied by linear and inverse
relationships and provides a similar fit to the data: R2 = 0.44,
compared to R2 = 0.23 for the linear and R2 = 0.47 for the inverse
forms. What adaptation function is most suitable remains an open
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NATURE CLIMATE CHANGE DOI: 10.1038/NCLIMATE1585
a
LETTERS
b
40° N
Latitude
Latitude
50° N
50° N
40° N
30° N
30° N
110° W
100° W
110° W
80° W
90° W
100° W
¬0.4
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Longitude
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0.1
0.2
0.3
Fractional yield change without adaptation
c
Latitude
80° W
90° W
Longitude
¬0.4
0.4
¬0.3
¬0.2
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0.0
0.1
0.2
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Fractional yield change with adaptation
50° N
40° N
30° N
110° W
100° W
90° W
80° W
Longitude
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
Fractional change with adaptation minus without adaptation
Figure 3 | Changes in yield from a 2 ◦ C warming. a, Without adaptation warming causes yield to decrease by 14% on average, although counties in the
deep south lose more than 50% of their yield, whereas those in the northwest increase by as much as 30%. The colour bar saturates at ±40% to highlight
variation across the middle range of counties. b, When adaptation is accounted for, warming is estimated to cause only a 6% average loss in yield. c, The
increase in yield brought about by adaptation relative to the no-adaptation scenario. The colour bar saturates at 10% to highlight variation across most
counties. As in Fig. 1, black borders indicate irrigated counties.
question, but any of these would serve to qualitatively illustrate
our basic point that plausible degrees of adaptation fundamentally
change predictions of yield response to moderate warming.
To explore the implications of the observed spatial adaptation to KDDs for the sensitivity of yield to warming, we
redefine β3 in equation (1) to follow the adaptation function
given by equation (2),
Y = β0 + β1 t + β2 GDD0 + (αo + αln(KDD) + η)KDD0 + (3)
In equation (3), as climatological KDDs increase with greater
warming, it is assumed that cultivar selection and management
practices are adjusted in keeping with the extant adaptation
observed across the US. Yield is solved for each county and each
year using the β, , α and η terms from equations (1) and (2) such
that, in the absence of any change in temperature, the original
yield data are recovered.
To illustrate the differences between non-adapted (equation (1))
and adapted (equation (3)) yield responses, it is useful to consider a
specific warming scenario, here taken to be a uniform 2 ◦ C warming,
which is often considered the safe limit of warming28 . Specifically,
we add 2 ◦ C to all temperature records, recalculate the GDD and
KDD terms from these warmer records but using the original
sample means to get new anomaly terms, and calculate a new
average yield for each county. Without adaptation, northwestern
regions broadly gain from warming because the benefits from
increased GDDs outweigh the losses from KDDs, whereas some
southern regions sustain losses of more than 50% because increased
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NATURE CLIMATE CHANGE DOI: 10.1038/NCLIMATE1585
KDDs reduce yield and low sensitivity to GDDs provides little
compensatory gain (Fig. 3a). Furthermore, warm regions will gain
KDDs more rapidly in response to uniform warming because
they have more days that already exceed the 29◦ threshold. The
(unweighted) average yield decrease across all counties is 14% for
a 2 ◦ C warming without adaptation.
This result is generally consistent with foregoing estimates,
although comparisons are limited by the fact that different spatial
averages are considered. One study6 found a 17% decline in global
average yields in response to a 2 ◦ C warming. Another study1 found
a 15% decline in an area-weighted average of eastern US yields.
Our calculations indicate only a 5% decrease in area-weighted
yields, but the lower value is expected because some of the hottest
states in the southeastern US are excluded from our study on
account of data regarding planting and harvest times not being
available. Note that all of these studies are essentially perturbation
approaches to calculating yield anomalies, and that the accuracy
of these estimates becomes increasingly questionable for larger
changes in temperature.
When adaptation is included, the average yield response to a
uniform 2 ◦ C warming is reduced from a 14% loss to one of 6%
(Fig. 3b,c; 95% c.i. −5 to −7%). Minnesota now stands to increase
yields by 11%; the yield losses from northern Ohio west to northern
Missouri are nearly eliminated; and North Carolina, Georgia and
east Texas reduce losses from 49% without adaptation to 39% with.
These last regions are already well above the optimal temperature
for present US maize production, and although the indication is
that adaptation can help, sizable losses are nonetheless incurred.
Already, many of the southern states are relatively unproductive
compared with the corn belt, and one consequence of increased
temperature could be migration of maize production towards
cooler latitudes. Another implication of low southern productivity
is that area-weighted yields (equivalent to fractional changes in
total production) go from a 5% decrease without adaptation to no
change with adaptation because gains in the highly productive corn
belt compensate for losses in the less productive south.
The adaptation function that we have empirically estimated
for a theoretical warming is consistent both with extant regional
adaptation and field trials of differing cultivars9 , but this analysis
omits other extenuating factors that may stymie or facilitate
adaptation. For example, reducing sensitivity to heat may entail
negative physiological trade-offs that reduce yields16 . To further
explore the issue of trade-offs, we extend equation (3) to include a
reduction in the positive effects of GDDs with warming that mirrors
the reduction in the negative effects of KDDs. A least-squares linear
fit indicates maladaptation for GDDs that average an order of
magnitude smaller than the positive adaptation found for KDDs
(Supplementary Figs S6 and S7). It follows that inclusion of GDD
maladaptation in our model leads to relatively small changes, and
we now obtain an 8% decline in average yield in response to a 2◦
warming, as opposed to a 6% decline when considering the basic
KDD-alone adaptation scenario. Inclusion of GDD maladaptation
also broadens the 95% confidence interval to 6–11% because of the
uncertainty in the GDD adaptation fit. This reduction in adaptability and increase in uncertainty does not change the conclusion
that adaptation offers the potential to substantially reduce damages
from a warming climate, but highlights how more work is needed
to constrain specific changes. Furthermore, there are also potential
benefits to warming that we have not included in our model, such as
greater flexibility in planting times15 , a longer growing season and
opportunities for cultivating new regions29 . Finally, note that most,
if not all, of these forms of adaptation can be implemented only in
a warmer climate, explaining why farmers that we expect to benefit
from adaptation have not yet made such changes.
Changes in water availability are another important consideration. Counties that irrigate more than 10% of their harvested
area have an average sensitivity to KDDs that is 0.08 (bushels per
acre)/KDD smaller than neighbouring counties without irrigation,
a difference that is highly significant (P < 0.01, using a one-sided
t -test, see Fig. 1b) and is in qualitative agreement with other
findings14,18 . Prize-winning yields from the 2010 to 2011 National
Corn Yield Contest also point to the importance of irrigation. For
unirrigated crops, the median prize-winning yields increase from
216 bushels per acre in the south, to 247 in the centre and 266 in
the north of the US (regional groupings follow that of a previous
study1 ). For irrigated crops, however, median southern yields are
260 bushels per acre, central yields are 267 and northern ones
are 247. The highest yields come from Texas with 370 bushels
per acre, showing that states with hot climatologies are capable of
attaining high yields.
We experimented with including a representation of precipitation in the model, but it negligibly influences model skill, even when
only non-irrigated crops are examined. The absence of significant
improvement may reflect that variations in precipitation are less
important for determining maize yield than temperature30 but
probably also results from a strong covariance between temperature and precipitation that makes inclusion of the latter partially
redundant. Precipitation is negatively correlated with maximum
daily temperatures everywhere in our study domain (Supplementary Fig. S8), as may be expected from the effects of clouds and
evaporable soil moisture. This anti-correlation reaches values of
−0.8 in some southern regions. The coincidence of high KDDs and
reduced water availability underscores that the low sensitivity to
KDDs found in southern regions reflects substantial adaptation.
It also suggests that our empirically fitted adaptation function
partially accounts for the expectation that warming will cause dry
regions to become drier31 , although further explicit examination of
the influences of water availability on yield is necessary.
Losses to US maize yield from increased temperature are almost
certainly overestimated if adaptation is not accounted for1,7 , and
here we have shown that adaptation could decrease the average
fractional losses in the Eastern US by roughly a factor of two and
could negate losses with respect to total production, at least for
a modest 2 ◦ C warming. The prospect that adaptation could have
such a significant influence on future yields provides impetus for
further study. Trials growing crop varieties in different conditions
of temperature and water availability, analysis of the sensitivity and
adaptability of other major food crops and other growing regions,
and the application of more complete biophysical models of crop
interactions with environmental variations would all be prudent
undertakings for adequately predicting the ecological response of
crops to a changing climate.
4
Methods
The data included in this study are from states that report maize planting
and harvest times for at least eight years, limiting the pool to 19 states in the
eastern United States. Temperature records are screened to include only those
having fewer than eight consecutive days of missing temperature values, with
the remaining gaps infilled using linear interpolation. Data from 78 counties
are also omitted because yield or nearby weather station records have less than
eight years of usable data.
Reported confidence intervals account for uncertainties in fitting a particular
model to the observations, but do not account for uncertainties in model
formulation itself. Some indication of model uncertainty is provided by the
three functional forms discussed in regard to KDD sensitivity versus climatology
(Fig. 2) and by the inclusion of GDD maladaptation. A range of alternative data
selections and model configurations were also explored before those presented in
the main text were selected for their simplicity and descriptive skill, and here we
further describe the implications of those choices. Counties not significantly fitted
(P < 0.05) by equation (1) were omitted. Including all counties gave similar losses
from a 2 ◦ C warming of 11% without adaptation and 4% with, where the slight
reduction in sensitivity is consistent with equation (1) being less likely to obtain a
significant fit with counties that have low sensitivity to weather variations.
A range of KDD thresholds between 25 ◦ C and 35 ◦ C were also experimented
with for each county, as well as thresholds based on the 90th percentile
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NATURE CLIMATE CHANGE DOI: 10.1038/NCLIMATE1585
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of temperatures in each county, but these also gave little improvement in
fit (Supplementary Fig. S9). We found no clear spatial pattern in optimal
threshold values and, for consistency, selected the same threshold of
29 ◦ C used in previous studies1,19 . Calculating GDDs after capping daily
maximum temperatures at 29 ◦ C to exclude overlap with KDDs also had
little overall effect.
Inclusion of a freezing degree day term in equation (1) likewise gave negligible
improvement in the ability of the model to predict yield variations, presumably
because of the very few freezing days that occur during the growing season. Finally,
inclusion of linear and quadratic precipitation terms were experimented with but
gave negligible increases in the model fit, as discussed in the main text, and led to
many more counties being rejected because of an insignificant fit as a result of the
increased degrees of freedom.
Other studies used a logarithmic transformation of yield data, as opposed
to magnitudes, to minimize the influence from trends and regional differences
in yield1,2 . Repeating our analysis using logarithmically transformed yields gave
a similar relationship between climatological KDDs and the sensitivity to KDDs
(compare Supplementary Fig. S10 and Fig. 2) and lower yield losses of 11% without
adaptation and 2% with adaptation.
The above modifications regarding data selection and model configuration
that we explored lead to qualitatively consistent results, providing confidence that
adaptation has significant potential to mitigate yield losses from moderate
warming. Nonetheless, further research using alternative simple model
formulations, more complete biophysical models, and field trials to test
these models are all needed to better understand the effectiveness of and
scope for adaptation.
13. Schlenker, W. & Roberts, M. J. Reply to Meerburg et al.: Growing areas in Brazil
and the United States with similar exposure to extreme heat have similar yields.
Proc. Natl Acad. Sci. USA 106, E121 (2009).
14. Nelson, G. C. et al. Climate change: Impact on agriculture and costs of
adaptation. (International Food Policy Research Institute, 2009).
15. Deryng, D., Sacks, W. J., Barford, C. C. & Ramankutty, N. Simulating the
effects of climate and agricultural management practices on global crop yield.
Glob. Biogeochem. Cycles 25, GB2006 (2011).
16. Sinclair, T. R. Challenges in breeding for yield increase for drought. Trends
Plant Sci. 16, 289–293 (2011).
17. Easterling, W. E. in Handbook of Climate Change and Agroecosystems: Impacts,
Adaptation, and Mitigation (eds Hillel, D. & Rosenzweig, C.) Ch. 14 (Imperial
College Press, 2011).
18. Rosenzweig, C. & Parry, M. Potential impact of climate change on world food
supply. Nature 367, 133–138 (1994).
19. Roberts, M. & Schlenker, W. in The Economics of Climate Change, Adaptations
Past and Present (eds Libecap, G. & Steckel, R.) 225–252 (Univ. Chicago Press,
2011).
20. Quick Stats 2.0. United States Department of Agriculture/National Agriculture
Statistics Service; http://quickstats.nass.usda.gov
21. United States Historical Climatology Network;
http://cdiac.ornl.gov/epubs/ndp/ushcn/ushcn.html
22. Lobell, D. B. & Asner, G. P. Climate and management contributions to recent
trends in US agricultural yields. Science 299, 1032 (2003).
23. Wang, J. Y. A critique of the heat unit approach to plant response studies.
Ecology 41, 785–790 (1960).
24. Yan, W. & Hunt, L. A. An equation for modelling the temperature response of
plants using only the cardinal temperatures. Ann. Bot. 84, 607–614 (1999).
25. Evans, L. T. Crop Evolution, Adaptation, and Yield (Cambridge Univ. Press,
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26. Crafts-Brandner, S. J. & Salvucci, M. E. Sensitivity of photosynthesis in a C4
plant, maize, to heat stress. Plant Physiol. 129, 1773–1780 (2002).
27. Gardner, B. R., Blad, B. L. & Watts, D. G. Plant and air temperatures in
differentially-irrigated corn. Agr. Meteorol. 25, 207–217 (1981).
28. Richardson, K. et al. Synthesis Report from Climate Change: Global Risks,
Challenges, and Decisions (Univ. Copenhagen, 2009).
29. Ramankutty, N., Foley, J. A., Norman, J. & McSweeney, K. The global
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Received 30 January 2012; accepted 15 May 2012; published online
18 November 2012
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Acknowledgements
We thank A. Stine, M. Gilbert, A. Rhines, N. Arnold, M. Lin, D. Schrag, S. Myers,
D. Lobell, W. Schlenker, M. Roberts and J. Foley for their commentary and insights. E.E.B.
and P.H. received support from NSF award 0902374 and the Packard Foundation.
Author contributions
E.E.B. and P.H. contributed equally.
Additional information
Supplementary information is available in the online version of the paper. Reprints and
permissions information is available online at www.nature.com/reprints. Correspondence
and requests for materials should be addressed to E.E.B.
Competing financial interests
The authors declare no competing financial interests.
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